How to simulate static vs kinetic friction?
Numerically, static friction (and the transition between static and dynamic friction) is extremely difficult to model, because of the abrupt jump and the directional ambiguity at the threshold between moving and non-moving.
In general, most friction force models therefore actually set the force to zero around the point of zero velocity!
Keep in mind that the the Blender physics engine is not intended for scientific or engineering purposes. It is rather meant to be comparatively simple and fast.
Therefore, you may have to use creative fakery for the feeling of physical accuracy. Maybe simulate the objects (if necessary, separately), bake their trajectories to keyframe and tweak manually. Maybe you can also achieve more impressive results with softbody simulation instead of rigid body simulation.
Or use a dedicated multibody-simulation software (there are free packages out there, like https://projectchrono.org/), but those are way more complex than blender.